English

On Non-intersecting Arithmetic Progressions

Combinatorics 2007-05-23 v1 Number Theory

Abstract

We prove that if one has k non-intersecting arithmetic progressions of integers, with common differences 2 <= q_1,...,q_k <= x, then k < x exp((-1/6 + o(1)) sqrt(log x loglog x)). This improves a result of Szemeredi and Erdos.

Keywords

Cite

@article{arxiv.math/0208236,
  title  = {On Non-intersecting Arithmetic Progressions},
  author = {Ernie Croot},
  journal= {arXiv preprint arXiv:math/0208236},
  year   = {2007}
}

Comments

Submitted